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arXiv · 0910.0689

Extremal black holes and nilpotent orbits

Guillaume Bossard
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Abstract

The stationary solutions of a large variety of (super)gravity theories can be described within a non-linear sigma model G / H* coupled to Euclidean gravity in three-dimensions, for which G is a simple group and H* a non-compact real form of its maximal compact subgroup. The absence of naked singularities in four dimensions requires the G Noether charge in 3D to satisfy a characteristic equation that determines it in function of the mass, the NUT charge and the electro-magnetic charges of the solution. It follows that the Noether charge associated to extremal black holes must lie in a certain Lagrangian submanifold of a nilpotent orbit of G. Constructing a suitable parameterisation of this Lagrangian, we are able to determine the so-called `fake superpotential' that governs the radial dependency of the scalar fields.

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Guillaume Bossard. 2009-10-05. Extremal black holes and nilpotent orbits. https://doi.org/10.1142/9789814304634_0051

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